He didn't declare himself the winner. The voting system is a bit more complex and while it's possible to completely override the election results through the electoral college, usually what happens is that the blue candidate gets a lot more votes in populous states with big cities (California, NY, etc), but as soon as you're one vote ahead in a state, the extra million or 2 don't matter.

Something that's been proposed to combat this without moving to an entirely new model, is for states to no longer be all or nothing. Instead of candidate A getting 60% of the votes and 100% of the EC vote, they'd get 60% of the EC vote and the other guy would get 40%. Then all votes would matter, rather than only swing state votes.